To replace missing teeth, it belongs to prior art to implant into the jaw bone artificial dental implants made from titanium, ceramics or from another suited material. Sometimes however it is also necessary to remove again an existing dental implant such as when there is an inflammation or sleeping implant. In this case, the dental implant can be drilled out again, using a hollow bur such as a trephine bur the inner diameter of which is only slightly larger than the largest outer diameter of the dental implant. Then, this trephine bur is at first held onto the dental implant, relying on the visual judgment of the doctor, in such a manner that the trephine bur forms a surrounding grip, at least rudimentarily, around the upper part of the dental implant. During drilling, the trephine bur is then guided by the dental implant. However, sometimes, the drilling occurs slantwise so that, in some cases, the dental implant is even cut into pieces, which involves a complicated surgical intervention in order to remove the rests of the dental implant.